Questions tagged [hard-problem]

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9 questions
16 views

When does the SIS Lattice-problem start becoming easy (According to the parameters size)?

SIS Problem : Given $m$ uniformly random vectors $a \in Z_q^n$, grouped as the columns of a matrix $A \in Z_q^{n.m}$, find a nonzero integer vector $z \in Z^m$ with $||z|| \leq \beta \lt q$, such that ...
57 views

Can I connect the hardness of a linear short integer solution problem to that of SIS problem?

As we know, SIS problem is defined as: for a function $f_A(s)$=$As$, where $A$ is a fixed, randomly-chosen matrix in $\mathbb{Z}_q^{r \times n}$, it is hard to find elements $s \in \mathbb{Z}_q^{n}$ ...
150 views

How is the matrix A related to the lattice space L in SIS?

Is the matrix $A= (b_1|,...,|b_m)$ where B=$(b_1,...,b_m)$ is the basis of the lattice space, $L$(B)? Not sure if the answer is trivial however I'm having trouble seeing how SIS is a lattice hard ...
68 views

Global minimum based cryptography?

When using the Back propagation Algorithm for Machine Learning, it is often said finding the global minimum of a cost function over $\mathbb{R}^n$ is very hard, and as $n$ increases it gets even more ...
184 views

How hard is Self-DLOG?

This question while asking for something different brings up an intriguing problem: If you can find $x$ such that $x\equiv R^x\pmod p$ then you can break DSA. Now I thought that one might be able to ...
151 views

Universal forgery based on mathematical problem

It is known that DSA admits universal forgery under assumption that the Attacker can solve the equation $x\equiv R^x\pmod p.$ Are there any other protocols admitting universal forgery based on non-...
191 views

More general - what is the hard problem of recovering r from r*p mod q?

I would like to know the cryptographic hard problem that is most closely tied to recovering integer $r$ from the modular product $r\times p\mod q$. (This is a simplification of an earlier post that ...
I would like to know what cryptographic hard problem this reduces to. Select two large prime numbers $p$ and $q$, and let $N=pq$. Select a random positive integer $r$. Compute the encryption of ...
The Short Integer Solution (SIS) problem is to find, given a matrix $A \in \mathbb{F}_q^{n \times m}$ with uniformly random coefficients, a vector \$\mathbf{x} \in \mathbb{Z}^m \backslash \{\mathbf{0}\}...